Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories

Abstract

We study the mirror symmetry of abelian 3d $\mathcal{N}=2$ theories with mixed Chern-Simons levels by turning them into ${\mathcal{T}}_{A,N}$ theories that are defined as $N$ copies of $U(1)-[1]$ theory coupled together by mixed Chern-Simons levels $k_{ij}$. We find that ${\mathcal{T}}_{A,N}$ theories have many mirror dual theories with different mixed CS levels and FI parameters. As an example, we analyze $U(1{)}_k+N_C\mathbf{C}+N_{AC}\mathbf{AC}$ theories by transforming these theories into certain ${\mathcal{T}}_{A,N}$ theories and find many equivalent effective Chern-Simons levels. Finally, we analyze mirror symmetry for theories corresponding to knots. In this work we use sphere partition functions and vortex partition functions to derive dual theories.

arXiv comment43 pages, 8 figures

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• 3d $\mathcal{N}=2$ Brane Webs and Quiver Matrices
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